Cross Country or Nordic skiing and snowshoeing are a fantastic way to explore the natural landscape in winter. My favorite time to go out is when a good fluffy snow fall is occurring. It transforms everything into a completely magical world. While you can take off in any direction with skiis on your feet, you may want to stick to groomed trails or even take a guided course.
For the most organized of adventures and where you can rent and take a guided course all at the same time, you’ll want to head to Tamarack Cross Country Ski Center at the end of Main Street (becomes Lake Mary Rd). In the summer this road goes all the way to the Lakes Basin but in winter, the road is closed and groomed for Nordic skiing. TIP: the right side of the road is reserved for paying guests of Tamarack but the left side is reserved for public access so if you want to explore on your own, bring your own skiis and stay to the left.
Otherwise, you can rent skiis at most ski rental shops in town and go explore the trails at some of these other locations. Most are groomed but the upkeep is sometimes spotty. Some of my favorites are Shady Rest park behind the visitors center, The Sherwins out Sherwin Creek road, and Mammoth Crest out past the main lodge of Mammoth Mountain Ski area.
Check out this map at www.mammothtrails.org/activity/40/cross-country-skiing/